On Creating Mathematics-Revised

On Creating Mathematics-Revised - On Creating Mathematics:...

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On Creating Mathematics: What Arthur and Blaise never knew
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Informal questions for Mathematicians at parties: What was the title of your dissertation? (snicker-snicker) What was your research?… (i.e., What is left to study in mathematics? A new way to add or multiply? What exactly do mathematicians do?
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Mathematics is… The Science of Numbers Problem Solving Theorem Proving The Science of Reasoning The Science of Patterns (Keith Devlin)
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Mathematics is like… A language A science An art A process
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Mathematics is… Vast (Mac Lane’s Connections) Performed in a wide variety of ways By a wide variety of people (See overhead of the connections within Calculus; also the overhead on the historical development of Probability)
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What do mathematicians do? Add, Multiply, Subtract, Divide, etc. Do Algebra, Make Geometry T-Proofs Solve Problems, Model Nature Experiment, Conjecture, Prove Precisely identify assumptions (axioms) Precisely define terms Categorize, Classify, Generalize, Reason
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Is New Mathematics … Discovered, Invented, or Created?
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Keith Devlin on Mathematics: (The “Math Guy” with Scott Simon on NPR’s Weekend Edition) Mathematical Discovery/Creation April 17,1999 http://www.npr.org/ramfiles/wesat/19990417.wesat.17.ram Mathematics as a language related to music September 9, 2000 http://www.npr.org/ramfiles/wesat/20000909.wesat.15.ram February 24, 2001 http://www.npr.org/ramfiles/wesat/20010224.wesat.12.ram
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Keith Devlin on the Nature of Mathematics Mathematics is the Science of Patterns Not only the patterns of numbers (arithmetic)… But also the patterns of shapes (geometry), reasoning (logic), motion (calculus), surfaces and knots (topology), etc. Reference: Mathematics--The Science of Patterns: The Search for Order in Life, Mind and the Universe (Scientific American Paperback Library)
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Mathematics is like…Music Both appreciated by many professional scientists and mathematicians Similar tasks in learning: practice, drill, learn a language, learn to sight-read, learn aesthetics In Tasks and Roles: Teach/Study Compose (Experiment-Conjecture-Prove, Invent new mathematical ideas) Conduct (Seminar Presentation at a Conference) Perform (trained student of mathematics) Improvise (problem solve: do all of the above…)
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On Creating Mathematics… What Arthur and Blaise never knew…
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Blaise Pascal (1623-1662) French mathematician, philosopher, and religious figure Projective geometry Mechanical adding machine Religious perspective Source: http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pascal.html
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1642-1645 Designed a mechanical calculator to assist his father’s role of examining all tax records of the Province of Normandy. Provided a monopoly
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On Creating Mathematics-Revised - On Creating Mathematics:...

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